Browsing Mathematical, Computational and Experimental Neuroscience by Title
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Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations
(20201027)The higher Leray–Serre spectral sequence associated with a tower of fibrations represents a generalization of the classical Leray–Serre spectral sequence of a fibration. In this work, we present algorithms to compute higher ... 
Computing Multipersistence by Means of Spectral Systems
(20190708)In their original setting, both spectral sequences and persistent homology are algebraic topology tools defined from filtrations of objects (e.g. topological spaces or simplicial complexes) indexed over the set Z of integer ... 
ConductanceBased Refractory Density Approach for a Population of Bursting Neurons
(2019)The conductancebased refractory density (CBRD) approach is a parsimonious mathematicalcomputational framework for modeling interact ing populations of regular spiking neurons, which, however, has not been yet extended ... 
GrigorchukGuptaSidki groups as a source for Beauvile surfaces
(20200414)If $G$ is a GrigorchukGuptaSidki group defined over a $p$adic tree, where p is an odd prime, we study the existence of Beauville surfaces associated to the quotients of $G$ by its level stabilizers $st_G(n)$. We prove ... 
Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model
(20200907)Specific kinds of physical and biological systems exhibit complex MixedMode Oscillations mediated by foldedsingularity canards in the context of slowfast models. The present manuscript revisits these systems, specifically ... 
Metastable resting state brain dynamics
(20190906)Metastability refers to the fact that the state of a dynamical system spends a large amount of time in a restricted region of its available phase space before a transition takes place, bringing the system into another state ... 
Microbial production of advanced biofuels
(2021)Concerns over climate change have necessitated a rethinking of our transportation infrastructure. One possible alternative to carbonpolluting fossil fuels are biofuels produced from a renewable carbon source using engineered ... 
MultiGGS groups have the congruence subgroup property
(20181108)We generalize the result about the congruence subgroup property for GGSgroups to the family of multiGGSgroups; that is, all multiGGSgroups except the one defined by the constant vector have the congruence subgroup ... 
Neuronglial Interactions
(20200607)Although lagging behind classical computational neuroscience, theoretical and computational approaches are beginning to emerge to characterize different aspects of neuronglial interactions. This chapter aims to provide ... 
ProC congruence properties for groups of rooted tree automorphisms
(20181121)We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro$\mathcal{C}$ ... 
A roadmap to integrate astrocytes into Systems Neuroscience
(20190506)Systems Neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to ... 
Spikeadding and resetinduced canard cycles in adaptive integrate and fire models
(20210503)We study a class of planar integrate and fire (IF) models called adaptive integrate and fire (AIF) models, which possesses an adaptation vari able on top of membrane potential, and whose subthreshold dynamics is piece ... 
Targeting Impaired Antimicrobial Immunity in the Brain for the Treatment of Alzheimer’s Disease
(20210504)Alzheimer’s disease (AD) is the most common form of dementia and aging is the most common risk factor for developing the disease. The etiology of AD is not known but AD may be considered as a clinical syndrome with multiple ... 
Targeting Infectious Agents as a Therapeutic Strategy in Alzheimer’s Disease
(20200526)Alzheimer’s disease (AD) is the most prevalent dementia in the world. Its cause(s) are presently largely unknown. The most common explanation for AD, now, is the amyloid cascade hypothesis, which states that the cause of ... 
A theoretical approach for the electrochemical characterization of ciliary epithelium
(20200123)The ciliary epithelium (CE) is the primary site of aqueous humor (AH) production, which results from the combined action of ultrafiltration and ionic secretion. Modulation of ionic secretion is a fundamental target for ... 
Why we should use topological data analysis in ageing: Towards defining the “topological shape of ageing”
(20201027)Living systems are subject to the arrow of time; from birth, they undergo complex transformations (selforganization) in a constant battle for survival, but inevitably ageing and disease trap them to death. Can ageing be ...